Analytic singularities of the dynamical zeta function

We study the dynamical zeta function Z D ( s ) related to the periodic trajectories of the billiard flow for several disjoint strictly convex bodies in 3 . We show that the analytic properties of Z D ( s ) close to the line of absolute convergence Re s = s 0 are similar to the behaviour close to the line Re s = 1 of the inverse Q ( s ) = 1/ R ( s ) of the classical Riemann zeta function R ( s ).